Not quite sure I understand the details, but the Senate vote had to occur by a certain date in order for Kavanaugh to hear the next round of cases scheduled for the next Supreme Court session.
And thus the reason for postponement..to make sure he wont be a part of that
The next SCOTUS session starts on Monday 1 October 2018, with oral arguments for 2 cases occurring each day Monday-Wednesday. So that leaves only next week to get him confirmed and sworn in. If the committee vote is on Thursday and they can line up a Senate vote for Friday (which seems sporty given the elaborate rules of the Senate because there probably needs to be time for "debate"), he could be sworn in on Saturday or Sunday and be on the job on Monday.
So he will likely miss the first few days but he can catch up. He likely has not had time to preview those cases to be very much engaged in those oral arguments anyway.